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Potential and Kinetic Energy


What is a system?

A system is an object or a group of objects. It is a useful way

of thinking about some physics problems.

When something about a system changes, the way that

energy is stored in it can also change from one form

to another.

Energy can take many different forms. For example:

• moving objects have kinetic energy

• stretched or compressed objects have elastic

potential energy

• objects in a gravitational field have gravitational

potential energy.


Changes in energy

Can you describe the way that energy is changing in

these systems?

An arrow fired from a bow:

kinetic energy

gravitational

potential energy

elastic potential energy

An archer draws back the bow

string, storing elastic potential

energy. When they release it, the

arrow flies forwards and upwards.


Changes in energy


these systems?

kinetic energygravitational

potential energy

elastic potential energy

A basketball hitting the floor:

An athlete scores a basket. As the

basketball falls, its gravitational

potential energy is converted to

kinetic energy. It compresses

(squashes) when it hits the floor,

and the kinetic energy is stored as

elastic potential energy.


Changes in energy


these systems?

A car braking at a traffic light:

sound energy

heat (thermal) energy

kinetic energy

When the brakes are applied,

friction increases. The kinetic

energy of the wheels is transferred

into sound energy and heat

(thermal) energy.


Changes in energy


these systems?

Water boiling in an electric kettle:

sound energy

heat (thermal) energy

electrical energy

When the kettle is switched on,

current flows through the heating

element. Electrical energy is

converted into sound energy and

heat (thermal) energy.


When an object is lifted upwards, the force doing

the lifting does work against the force of gravity.

The work done is stored as gravitational

potential energy (Ep). It is called potential

energy because it has the potential to be

transferred into other forms of energy later.

For example, this crane does work lifting this box.

For example, if the hook broke and the box

fell, the stored gravitational potential energy

would be converted to kinetic energy.

What is gravitational potential energy?


How is GPE calculated?

The GPE of an object can be calculated using this equation:

GPE = mass × gravitational field strength × height

Height (h) is measured in metres (m).

Mass (m) is measured in kilograms (kg).

Gravitational potential energy (Ep) is measured in joules (J).

Gravitational field strength (g) is measured in newtons per

kilogram (N/kg), and is usually assumed to be 10N/kg

close to the surface of Earth.

Ep = mgh

or


Factors affecting GPE


A plane with a mass of

5,000kg travels at a height

of 10km above the ground.

Calculating GPE question 1

How much gravitational

potential energy does

the plane have?

= 5,000 ×10 × 10,000

GPE = mass × gravitational field strength × height

= 500,000,000J

Assume a value of 10N/kg

for g.

= 500MJ


An orange with a mass of 250g

falls 2.5m from its branch to

the ground.

Calculating GPE question 2

How much GPE will the orange

have lost when it hits the ground?

= 0.25 × 10 × 2.5

= 6.25J

= mass × gravitational field strength ×GPE

lost

change

in height

Assume a value of 10N/kg for g.


GPE, mass and height calculations


Kinetic energy is the

energy an object has

because it is moving.

What is kinetic energy?

The word ‘kinetic’ comes from the Greek word

‘kinesis’, meaning motion.

All moving things have kinetic energy, but the amount of

energy they have is not just dependent on how fast they

are moving.

What other factors might affect the kinetic energy of

a moving object?


How is kinetic energy calculated?

The kinetic energy (Ek) of an object can be calculated

using this equation:

Velocity, v, is measured in metres per second (m/s).

Mass, m, is measured in kilograms (kg).

Kinetic energy, Ek, is measured in joules (J).

Ek = ½ × mass × velocity2

Ek = ½mv2

or


kinetic energy = ½ × mass × velocity2

A car with a mass of 1,000kg

travels at a velocity of 20m/s.

Calculating kinetic energy question

What is the kinetic energy

of the car?

= 200,000J = 200kJ

= ½ × 1,000 × 202


If you know the kinetic energy of an object, you can rearrange

the equation in order to calculate its mass or velocity.

Ek = ½mv2

Rearranging the kinetic energy equation

v = 2Ek

mm =2Ek

v2

Rearranged to

calculate mass:

Rearranged to

calculate velocity:


A lorry has a mass of 20,000kg.

If its kinetic energy is 2.25MJ,

at what velocity is it travelling?

Calculating velocity question

Ek = ½mv2

= 15m/s

velocity =

=


Using the kinetic energy equation


Energy transfers within a system

Imagine a tennis ball with a mass of 60g dropped from

a height of 50cm.

h = 0.5m

m = 0.06kgInitially, the tennis ball has

some gravitational

potential energy (Ep):

Ep = mgh

= 0.06 × 10 × 0.5

= 0.3J

And no kinetic energy (Ek),

because it is not moving.

The total energy in the system is 0.3J.


total energy = 0.3J

Ek = 0J

Ep = 0.3J

Ek = 0.1J

Ep = 0.2J

total energy = 0.3J

Ek = 0.2J

Ep = 0.1J

total energy = 0.3JEk = 0.3J

Ep = 0J

total energy = 0.3J

Imagine a tennis ball with a mass of 60g dropped from

a height of 50cm.

Energy transfers within a system

When it is dropped, Ep is

converted to Ek.

When it hits the ground, Ep

is reduced to zero. All of

the gravitational potential

energy has been transferred

to kinetic energy.

As it falls, Ep decreases

and Ek increases, but the

total energy of the system

stays the same.


Energy transfers in rollercoasters

What happens to the Ek and Ep of a rollercoaster?


As the rollercoaster loses height, the stored gravitational

potential energy is transferred into kinetic energy.

This equation is only true if air

resistance and friction are ignored.

Ep lost = Ek gained

The relationship between GPE and KE

In reality, Ep would also be

transferred into heat and

sound energy, so the Ek of

the rollercoaster would be

a bit less than the Ep lost.


Energy transfer of roller coasters


Terminal velocity


Glossary


Multiple-choice quiz

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